The effects of a specularly reflecting surface on the wall heat flux and medium temperature distribution are studied. The system is an infinite square duct enclosing an absorbing and emitting medium. The walls are opaque, and black or gray. The walls emit diffusely but reflect diffusely or speculary. Heat is transferred by the combined effect of conduction and radiation. The radiative heat transfer is analyzed using direct discrete-ordinates method. The parameters under study are conduction, to radiation parameter, optical depth, wall emissivity, and reflection characteristics. The specular reflection and diffuse reflection show sizeable differences when the conduction to radiation parameter is less than around 0.01. The differences appear only either on the side wall heat flux or on the medium temperature profiles for the range of this study. The differences on the side wall heat flux are observed for optical thickness less than around 0.1 However the differences on the medium temperate profiles are found for optical thickness greater than around 1. The difference increase with increasing reflectance. The specular reflection increases the well heat flux gradient along the side wall.